where \(d_g\)  is the geodesic distance between \(x\)  and the \(1.0{m}\)  success zone surrounding the nearest object from category \(o_t\)  (similar to [1]}), and \(d_{\textrm {max}} = 10{m}\)  is the distance at which \(U_t^o\)  decays to 0, selected via validation experiments.
